Some employers use lie detector tests to screen job applicants. lie detector tests are not completely reliable. suppose that in a lie detector test, 65% of lies are identified as lies and that 14% of true statements are also identified as lies. a company gives its job applicants a polygraph test, asking "did you tell the truth on your job application? ". suppose that 93% of the job applicants tell the truth during the polygraph test. what is the probability that a person who fails the test was actually telling the truth? round to three decimal places as needed. (hint: divide the probability that a person told the truth and failed the test by the probability that a person failed the test.)

The probability that a person who fails the test was actually telling the truth is 0.741

Step-by-step explanation:

For calculate this probability is necessary to divide the probability that a person told the truth and failed the test by the probability that a person failed the test.

Lets call P1, the Probability that a person told the truth and failed the test. It is the multiplication of:

P1 = 0.93*0.14 = 0.1302

Where 0.93 is the percentage of jobs applicants who tell the truth and 0.14 is the proportion of true statements that are identified as lies.

Let's call P2, the probability that a person failed the test. This probability is calculated in two parts:

        0.07*0.65=0.0455

Where 0.07 is the percentage of jobs applicant who didn't tell the truth and 0.65 is the proportion of lies that are identified as lies.

So, P2 is the sum of the 2 cases and it is:

P2=0.1302+0.0455=0.1757

Then the probability that a person who fails the test was actually telling the truth is:

P=P1/P2

P=0.1302/0.1757

P=0.741

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